Convex Optimization: Theory, Methods and Applications - Couverture souple

Couverture souple

ISBN 10 : 153614696X ISBN 13 : 9781536146967

Editeur : Nova Science Publishers Inc, 2019

Synopsis

Over the past two decades, it has been recognized that advanced image processing techniques provide valuable information to physicians for the diagnosis, image guided therapy and surgery, and monitoring of human diseases. This book introduces novel and sophisticated mathematical problems which encourage the development of advanced optimisation and computing methods, especially convex optimisation. The authors go on to study Steffensen-King-type methods of convergence to approximate a locally unique solution of a nonlinear equation and also in problems of convex optimisation. Real-world applications are also provided. The following study is focused on the design and testing of a Matlab code of the Frank-Wolfe algorithm. The Nesterov step is proposed in order to accelerate the algorithm, and the results of some numerical experiments of constraint optimization are also provided. Lagrangian methods for numerical solutions to constrained convex programs are also explored. For enhanced algorithms, the traditional Lagrange multiplier update is modified to take a soft reflection across the zero boundary. This, coupled with a modified drift expression, is shown to yield improved performance. Next, Newton s mesh independence principle was used to solve a certain class of optimal design problems from earlier studies. Motivated by optimization considerations, the authors show that under the same computational cost, a finer mesh independence principle can be given than before. This compilation closes with a presentation on a local convergence analysis for eighth order variants of Hansen Patrick s family for approximating a locally unique solution of a nonlinear equation. The radius of convergence and computable error bounds on the distances involved are also provided.

Détails de l'édition

• Éditeur: Nova Science Publishers Inc
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 153614696X
• ISBN 13: 9781536146967
• Reliure: Broché
• Nombre de pages: 158
• Éditeur: Ruud Arto
• Coordonnées du fabricant: non disponible